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We present a general theory of the holographic image reconstruction with linear frequency modulation (LFM) radars. For the first time, the system limitations in terms of the object extent and distance are derived and explicitly related to the LFM radar frequency-modulation slope $\gamma $. The holographic inversion formula is improved to account for the spherical spread of the scattered wave. The theory and the generalized holographic inversion algorithm are validated by synthetic benchmark data as well as experimental data from an in-house LFM-radar prototype operating at 29.9-GHz central frequency and bandwidth of 5.8 GHz. Experiments confirm that the lateral spatial resolution is about 5 mm. For optimal performance, the system is calibrated using a simple but effective calibration approach based on a measurement with a metallic plate. Experiments, with a volunteer carrying metallic and nonmetallic objects, demonstrate very good performance in realistic scenarios. [ABSTRACT FROM AUTHOR]